PET Image Reconstruction With Kernel and Kernel Space Composite Regularizer

Led by the kernelized expectation maximization (KEM) method, the kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction variance and high sensitivity to iteration numbers, and the difficulty in preserving image details and suppressing image variance simultaneously. To solve these problems, this paper derives, using the ideas of data manifold and graph regularization, a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction. The composite regularizer consists of a convex kernel space graph regularizer that smooths the kernel coefficients, a concave kernel space energy regularizer that enhances the coefficients’ energy, and a composition constant that is analytically set to guarantee the convexity of composite regularizer. The composite regularizer renders easy use of PET-only image priors to overcome KEM’s difficulty caused by the mismatch of MR prior and underlying PET images. Using this kernel space composite regularizer and the technique of optimization transfer, a globally convergent iterative algorithm is derived for RKEM reconstruction. Tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm, and demonstrate its better performance and advantages over KEM and other conventional methods.